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Tensor

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DifferentialGeometry/Tensor/AdaptedNullTetrad
find a null tetrad which transforms the Newman-Penrose Weyl scalars to a standard form

DifferentialGeometry/Tensor/AdaptedSpinorDyad
find a spinor dyad which transforms the Weyl spinor to normal form

DifferentialGeometry/Tensor/BachTensor
calculate the Bach tensor of a metric

DifferentialGeometry/Tensor/CanonicalTensors
create various standard tensors

DifferentialGeometry/Tensor/CheckKillingTensor
check that a tensor is the Killing tensor for a given metric or connection

DifferentialGeometry/Tensor/Christoffel
find the Christoffel symbols of the first or second kind for a metric tensor

DifferentialGeometry/Tensor/ConformalKillingVectors
calculate the conformal Killing vectors for a given metric

DifferentialGeometry/Tensor/CongruenceProperties
calculate properties of a congruence of curves

DifferentialGeometry/Tensor/Connection
define a linear connection on the tangent bundle or on a vector bundle

DifferentialGeometry/Tensor/ContractIndices
contract the indices of a tensor

DifferentialGeometry/Tensor/CottonTensor
calculate the Cotton tensor for a metric

DifferentialGeometry/Tensor/CovariantDerivative
calculate the covariant derivative of a tensor field with respect to a connection

DifferentialGeometry/Tensor/CovariantlyConstantTensors
calculate the covariantly constant tensors with respect to a given metric or connection

DifferentialGeometry/Tensor/CurvatureTensor
calculate the curvature tensor of a linear connection on the tangent bundle or on a vector bundle

DifferentialGeometry/Tensor/DirectionalCovariantDerivative
calculate the covariant derivative of a tensor field in the direction of a vector field and with respect to a given connection

DifferentialGeometry/Tensor/EinsteinTensor
calculate the Einstein tensor for a metric

DifferentialGeometry/Tensor/FactorWeylSpinor
factorize a rank 4 symmetric spinor

DifferentialGeometry/Tensor/FormInnerProduct
compute the inner product of two forms with respect to a given metric tensor

DifferentialGeometry/Tensor/GRQuery
check various geometric properties of fields on a spacetime

DifferentialGeometry/Tensor/GenerateSymmetricTensors
generate a list of symmetric tensors from a list of tensors

DifferentialGeometry/Tensor/GenerateTensors
generate a list of all product tensors from a list of lists of tensors

DifferentialGeometry/Tensor/GeodesicEquations
calculate the geodesic equations for a symmetric linear connection on the tangent bundle

DifferentialGeometry/Tensor/HodgeStar
apply the Hodge star operator to a differential form

DifferentialGeometry/Tensor/HomothetyVectors
calculate the homothety vectors for a given metric

DifferentialGeometry/Tensor/IndependentKillingTensors
given two lists R and S of rank p Killing tensors, find a maximal sublist T of R such that the combined list of tensors [T, S] are linearly independent (over the real numbers)

DifferentialGeometry/Tensor/InfinitesimalHolonomy
find the matrix Lie algebra giving the infinitesimal holonomy of a metric or a connection on the tangent bundle or on a general vector bundle

DifferentialGeometry/Tensor/InvariantTensorsAtAPoint
find tensors or differential forms which are invariant under the infinitesimal action of a set of matrices

DifferentialGeometry/Tensor/InverseMetric
find the inverse of a metric tensor

DifferentialGeometry/Tensor/KillingBracket
a covariant form of the Schouten bracket for symmetric tensors

DifferentialGeometry/Tensor/KillingSpinors
calculate the Killing spinors for a given spacetime

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